On optimal domestic processing of exhaustible natural resource exports (Q1111914)

This paper is concerned with the desirability of domestic processing of natural resource exports from a small open economy completely dependent upon these exports. In the framework of a melleable capital model, where the services of imported capital are needed to process the resource domestically, the paper examines the optimal rates of extraction, domestic processing and import of capital services in different economic scenarios, defined in terms of processing technology, cost and market structures, presence or absence of taxes and subsidies, historical growth in prices, etc. This is achieved through analyzing different variants of the optimal control problem. \[ _{x(t),\mu (t),K(t)}\int^{\infty}_{0}U[C(t)]\overline{e}^{\delta t}dt \] \[ \text{ subject to }C(t)=P_ 1[1-\mu (t)]+P_ 2F[(K(t),\mu (t)x(t)]- rK(t), \] \(\dot S(t)=-x(t)\), \(S(0)=S_ 0>0\), \(x\geq 0\), \(K(t)\geq 0\), \(C(t)\geq 0\), \(0\leq \mu \leq 1\), where \(P_ 1(P_ 2)=\) price of raw (processed) resource, \(x=\) extraction rate, \(\mu=\) proportion processed, \(K=\) capital, \(S=\) stock, \(C=\) consumption, \(r=\) rental of capital, \(F=\) production function, and \(U=\) utility. It is shown that barring the special case of the linear, homogeneous function \(F(.,.)\), some level of domestic processing is always socially optimal. Morever, the level of domestic processing will tend to rise over time to full and complete processing as the resource stock moves towards exhaustion. It is also argued that in the case of a linear homogeneous function \(F(.,.)\), explicit consideration of transportation costs, market power, productivity growth, and tax-cum-subsidies policy tend to bring about a phase of partial domestic processing.